Resolution[J. A. Robinson, A machine oriented logic based
on the resolution principle, Journal of the ACM, 12, No. 1, 1965.]
is a method of proof by contradiction.

Given a set of premises F1 &and F2 &and ... &and Fn
and a desired conclusion G, we prove that
F1 &and F2 &and ... &and Fn &and &not G is inconsistent.
This is done by adding new clauses Hi, each of which is a logical
consequence of the existing clauses, to the set. If we can add □
as a new clause, then the whole formula collapses to false and is thus
inconsistent.

Theorem: If H is a logical consequence of F, F &and H = F.
Proof: If F is false, then both sides are false. If F is true, then
H must be true, so F &and H is true.

Thus, we are justified in adding any logical consequence of our set of
formulas to the set without changing its truth value.